Anova unequal variance

Hi:

On Thu, Jan 21, 2010 at 12:29 PM, Peng Yu <pengyu.ut at gmail.com> wrote:

On Thu, Jan 21, 2010 at 2:16 PM, Dennis Murphy <djmuser at gmail.com> wrote:

Hi:

This paper was a prelude to his first book 'Exact Statistical Methods
for
Data Analysis'.
He uses what is called a generalized p-value approach to inference, and
for
the
book he wrote commercial software. AFAIK, no R package implements his
methodology. The 'conventional' approach to unequal variance in ANOVA is
to use generalized least squares, whose implementation is found in gls()
in
the nlme package.

There are quite a few references on ?gls. Which one is the most
introductory material that I should start with, if I want to
understand the method?

GLS is a standard technique in linear model theory. It is well documented.
Any good book on linear statistical models should have a discussion on it.
(Probably Wikipedia, too). If unequal
variance is the only issue (meaning independent observations), the technique
is called weighted least squares (WLS). GLS is more general in that it can
be applied to correlated observations. Assuming the variances are known
(a big if), it is easy to convert from WLS to ordinary least squares -
divide all
the responses by the group standard deviation to which it belongs. The
transformation in GLS (again, assuming variances known) involves a matrix
transformation (Cholesky, when appropriate). When the variances are unknown,
as they usually are, the estimation problem is a lot messier and one needs
to resort to approximations.

Do you have any simple explanation that may help me understand what is
the difference between the method in 'Exact Statistical Methods for
Data Analysis' and the method in gls()?

No. They're quite different approaches. Weerahandi's is conditional;
GLS is unconditional.

Dennis

HTH,
Dennis

On Thu, Jan 21, 2010 at 12:03 PM, Peng Yu <pengyu.ut at gmail.com> wrote:

I found this paper on ANOVA on unequal error variance. Has this be
incorporated to any R package? Is there any textbook that discuss the
problem of ANOVA on unequal error variance in general?

http://www.jstor.org/stable/2532947?cookieSet=1